I would say a 4670 isn't powerful enough to run games at a high enough resolution for the memory to be the deciding factor in performance so there is probably little to no drawback in real life. It all depends on what resolution and what particular software you are trying to run though.
For higher resolutions you need more memory, but there are cards that are based on gimmick. For example, you get a GT210 from nvidia which might have 512mb of VRAM, but the processor the card is not powerful enough to use all of it. Heck, even 256mb for that GPU will suffice
In your case, you will see exact performance with 1gb or with 512mb versions of 4670.
Uptil a resolution of 1600x1020, 512 mb is enough as the CPU can take the stress till that. However, push your resolution over that and you'll be better off with a 1gb card because that's where the GPU memory gets utilized. Leaving your CPU to handle high resolutions isn't a good idea coz the CPU can't take it which is why the GPU compensates by utilizing the extra 512mb.
So if you're looking at gaming at a resolution of 1920x1080, you're gonna be better off with 1gb of GPU memory as against 512mb
The 1 gb card will have an advantage only if you're gaming at a higher resolution (1920x1080). 512 mb card's can handle resoltions upto that, but with the 4670 it might be stretching it. While the card does support resolutions upto 2560 x 1600, you might wanna take the 1gb card to be safer.
Keep in mind that the card will run games like COD:MW at playable frames, it will not run Crysis (DX10) at more than 23fps
Just to say that in the main whats been said is all correct but games these days like throwing large textures about and if you can affrod the 1GB then it will be worth your while getting it. If they want to charge a lot more then no but if its a small differance then you are definatly better off getting the 1GB card.